Answer:
The value is [tex] E(k) = \frac{68}{52}[/tex]
Step-by-step explanation:
From the question we are told that
The total number of cards is [tex]n = 52[/tex]
Let k represent the winnings and loss when any card is drawn
So k = $5 when a faced card is drawn
So k= $ 20 when an Ace card is drawn
So g = - $2 when any other card is drawn
Generally in a standard deck of card
The number of Ace is 4
The number of queen is 4
The number of jack is 4
Therefore the number off faced cards is
R = 4 + 4 + 4 = 12
Generally the number of other cards is
Y = n - R
=> Y = 52 - 12
=> Y = 36
Generally the probability of drawing a faced card is mathematically represented as
[tex]P(k = 5) = \frac{ 12}{52}[/tex]
Generally the probability of drawing a Ace card is mathematically represented as
[tex]P(k = 20) = \frac{ 20}{52}[/tex]
Generally the probability of drawing a other card is mathematically represented as
[tex]P(k = -2) = \frac{ 36}{52}[/tex]
Generally the expected profit from any one draw is mathematically represented as
[tex]E(k) = \sum k_i * P(K = k)[/tex]
=> [tex]E(k) = 5 * \frac{ 12}{52} + 20\frac{ 20}{52} + [- 2 * \frac{ 36}{52}][/tex]
=> [tex] E(k) = \frac{68}{52}[/tex]
